An efficient quasi-Newton method for two-dimensional steady free surface flow

Toon Demeester (Corresponding author), E. Harald van Brummelen, Joris Degroote

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

6 Citaten (Scopus)


Steady free surface flows are of interest in the fields of marine and hydraulic engineering. Fitting methods are generally used to represent the free surface position with a deforming grid. Existing fitting methods tend to use time-stepping schemes, which is inefficient for steady flows. There also exists a steady iterative method, but that one needs to be implemented with a dedicated solver. Therefore a new method is proposed to efficiently simulate two-dimensional (2D) steady free surface flows, suitable for use in conjunction with black-box flow solvers. The free surface position is calculated with a quasi-Newton method, where the approximate Jacobian is constructed in a novel way by combining data from past iterations with an analytical model based on a perturbation analysis of a potential flow. The method is tested on two 2D cases: the flow over a bottom topography and the flow over a hydrofoil. For all simulations the new method converges exponentially and in few iterations. Furthermore, convergence is independent of the free surface mesh size for all tests.

Originele taal-2Engels
Pagina's (van-tot)785-801
Aantal pagina's17
TijdschriftInternational Journal for Numerical Methods in Fluids
Nummer van het tijdschrift7
Vroegere onlinedatum9 jan. 2020
StatusGepubliceerd - 1 jul. 2020


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